How am I supposed to differentiate between each case?

Once completed, the top side in each case will be yellow. Knowing that, it is possible to recognize each case based on the relationship the non yellow colors have (opposite colors, same colors, or adjacent colors).

If you need further explanation, Rowe and Rowan explain this recognition system very well in their videos.

Sune Cases

R U R' U R U2 R'

U' L' U R2 U' L U2 R' U' R2

R U' L' U R' U' L

F R' F' R U2 R U2 R'

L' U2 L U2 L F' L' F

U2 R U' R U' R' U R' U' y R U' R'

Antisune Cases

L' U' L U' L' U2 L

U2 R U2 R' F R' F' R U' R U' R'

L' U R U' L U R'

F' L F L' U2 L' U2 L

R U2 R' U2 R' F R F'

U2 F R F' U R U' R U R' U R'

Note: It is pretty easy to reflect the first, third, fourth, and fifth Antisune algorithm listed. Plus, the other two have AUFs, so I recognize the cases from the position given or the opposite (a U2 away), depending on how it ends up positioned after solving the first layer. To solve the case from the other position simply reflect the algorithm you know if it's one of those four listed, or just AUF and do the standard algorithm. For example, the first case changes from L' U' L U' L' U2 L to R' U' R U' R' U2 R.